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An aluminium plate foxed in a horizontal position has a hole of diameter 2.000 cm. A steel sphere of diameter 2.005 cm rests on this hole. All the lengths refer to a temperature of 10 degree celsius. The temperature of the entire system is slowly increased. At what temperature will the ball fall down? Coefficient of aluminium is 23x10^-6/degree celsius and that of steel is 11x10^-6/degree celsius.
Dear Cathy,
It will pass through the hole when the diameter of both of them are same.
Let it happens at temperature t degree.
For steel, V=Vi(1+Υt)
Vi=initial vol
Y=coeff of vol expansion.
For Al A=Ai(1+βt)
Ai=initial area.
we have considered the vol of steel ball but the area of the Al plate as it's a 2D body.
again at the required temperature radii will be the same. hence putting v=4/3∏(r)^3 & A=∏(r)^2 we get
t=218.8 degree
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Regards,
Askiitians ExpertsSoumyajit Das IIT Kharagpur
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